There are two very different aspects that need to be met by number of encounters per day.
One of them is challenge. And yes, you can have fewer, deadlier encounters and reach your goals for this. This isn't really debated, and it's the primary - on only - one that most people think about.
The other one is balance between the at-will classes like rogue or the EB-focused warlock, and the long-rest recovery classes like full casters plus hybrids like the barbarian or the paladin.
If you took your average full caster and took away all slots, they would be less effective on average than at-will classes like the rogue. At-will > cantrip. (This doesn't include EB boosted with invocations.)
On the other hand, if you gave casters unlimited of their highest level slots, they would do more than at-will characters. A fireball with multiple opponents, etc. Slots of the highest few levels > at-will.
Putting them together, we get, in generic terms for the average character:
Slots of the highest few levels > at-will > cantrip
So in order to balance these, we need some number of spells cast using highest level slots, and some cantrips or low-impact spells (like 1st level offensive spells in T2+). Some above and some below will average out to the same as an at-will.
Let's examine that. If you run a few encounters and run the party's casters all the way out of spells - you are STILL not balancing the classes unless you also are forcing them to have a good number of rounds at less than at-will effectiveness.
An easy way to work this out is average effectiveness per action, over the course of the adventuring day.
Ah, so if you have fewer encounters, as long as the last as long as more encounters we're good, right?
Well, no. It's moving in the right direction, but duration is a thing. If an encounter is 3-4 rounds and you can a spell lasting 1 minute, you only get 3-4 rounds of it at most. But if the combat lasts 9 rounds, then you are getting 2-3 times the effect from the same slot and the same action. It's more powerful. So you need to offset it with even more rounds of lower than at-will efficiency.
A easy way to see this is the barbarian. Say you've got 3 rages per day. Assuming the encounters total to the same deadliness, is there any case where you are worse off if you can rage for every encounter instead of half of them? That's one of the things that decreasing the number of encounters does - allows duration effects to be even more powerful.
To sum up:
1. Can balance danger and challenge in fewer encounters by having tougher encounters.
2. Need to have more total rounds fighting in fewer encounters that all of the more encounters in order to maintain balance between classes.
And that second one does not often get met. Fewer encounters per day is usually fewer total rounds then if we did all of the encounters per day, and that definitely is mathematically biased in terms of the long-rest-recovery classes like casters as well as a big boost for hybrids like the barbarian and the paladin.